Question

gives the acceleration a versus time t for a particle moving along an x axis. The a-axis scale is set by as = 14.0 m/s2. At t = -2.0 s, the particle's velocity is10.0 m/s. What is its velocity at t = 6.0 s?

Answer 1

Slope = da/dt = -56/4 = -14 since each vertical division is 14
a = -14 t + C
at t = 0 a = 56
a = -14 t + 56 = dv/dt
v = -7 t^2 + 56 t + C2
At t = -2 v = 10 so C2 = 150
v = -7 t^2 + 56 t + 150
At 6 sec
v = -7 * 36 + 336 + 150 = 234 m/s